1. Multiplying Decimals Lesson 3.4

2. Using Base Ten Blocks • The flat represents 1, the rod represents 0.1 and the small cube represents 0.01 • By using Base Ten Blocks to make a rectangle, you can switch to addition instead of multiplication for decimals.

3. Modeling • A rectangular park measures 1.7 km by 2.5 km. Step 1: Build a rectangle with length of 2.5 and width 1.7 Width (1.7 km) When the rectangle is finished, count the blocks in the rectangle. Length (2.5 km)

4. There should be 2 flats: 2 x 1 = 2 • There should be 19 rods: 19 x 0.1 = 1.9 • There should be 35 cubes: 35 x 0.01 = .35 • The total area will be: 2 + 1.9 + .35 = _________

5. But How Do I Multiply?? • 1.7 x 2.5 • Pretend there are no decimals. • 17 x 25 • Multiply as normal. • Then add the decimal after.

6. But Where Do I Put The Decimal? 1.7 x 2.5 1.7 x 2.5 4.25 Ask yourself, “How many numbers are after the decimal?” = 1 Ask yourself, “How many numbers are after the decimal? = 1 There are 2 numbers total after the decimal point. Start at the end of the number, then, move two numbers to the left. Where you stop the decimal goes.

7. How Do I Multiply 2 Two Digit Numbers? • A brief reminder... 13 x 12 26 190 216 1) Multiply 3 x 2 first. Put the answer below the 2. (6) 2) Then, multiply 2 x 1. Put the answer beside the 2 and under then 1. (2) 3) Then, put a zero under the 2. (0) 4) Then multiply 1 x 9. Put the answer beside the zero and under the 1. (9) 5) Then, multiply 1 x 1. Put this answer beside the 9. 6) Add the two numbers together to get your answer.

8. Try these with long multiplication. • 14 x 21 • 17 x 12 • 15 x 20

9. Word Problems • At the Farmers Market, 1 kg of grapes costs $2.95. How much would 1.8 kg of grapes cost? • 1 kg of grapes costs $2.95. • So, 1.8 kg would cost 2.95 x 1.8 Create a rectangle model (Base Ten)

10. 2.95 x 1.8 • (2.0 x 1.0) + (0.95 x 1.0) + (2.0 x 0.8) + (0.95 x 0.8) • (2 x 1) + (0.95) + (2 x 0.8) +(0.95 x 0.8) • 2 + 0.95 + 1.6 + 0.76 = 5.31 Therefore, 1.8 kg of grapes would cost $5.31. 2.95 2.0 x 1.0 0.95 x 1.0 1.8 2.0 x 0.8 0.95 x 0.8

11. A kg of apples costs $1.90. • How much would 2.1 kg of apples cost? • Draw the rectangle model and solve.

12. An area rug is rectangular. Its dimensions are 3.4 m by 2.7 m. • Solve using multiplication.

13. Estimation • To estimate using multiplication, multiply the two whole numbers together. (First round up or down to the nearest whole number) • 5.3 x 2.1 = 5 x 2 = 10 • A good estimation is 10. • Multiply to verify your estimation.

14. Use estimation, then solve using multiplication. Remember to round up or down to the nearest whole number) • 2.6 x 1.3 • 7.2 x 4.8 • 3.9 x 3.2

15. Homework • Workbook 3.4 • Textbook Page 102 – 103 # 4, 5, 9, 10 and Reflect